8n-n^2=32n-144-2n^2

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Solution for 8n-n^2=32n-144-2n^2 equation:


Simplifying
8n + -1n2 = 32n + -144 + -2n2

Reorder the terms:
8n + -1n2 = -144 + 32n + -2n2

Solving
8n + -1n2 = -144 + 32n + -2n2

Solving for variable 'n'.

Reorder the terms:
144 + 8n + -32n + -1n2 + 2n2 = -144 + 32n + -2n2 + 144 + -32n + 2n2

Combine like terms: 8n + -32n = -24n
144 + -24n + -1n2 + 2n2 = -144 + 32n + -2n2 + 144 + -32n + 2n2

Combine like terms: -1n2 + 2n2 = 1n2
144 + -24n + 1n2 = -144 + 32n + -2n2 + 144 + -32n + 2n2

Reorder the terms:
144 + -24n + 1n2 = -144 + 144 + 32n + -32n + -2n2 + 2n2

Combine like terms: -144 + 144 = 0
144 + -24n + 1n2 = 0 + 32n + -32n + -2n2 + 2n2
144 + -24n + 1n2 = 32n + -32n + -2n2 + 2n2

Combine like terms: 32n + -32n = 0
144 + -24n + 1n2 = 0 + -2n2 + 2n2
144 + -24n + 1n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
144 + -24n + 1n2 = 0

Factor a trinomial.
(12 + -1n)(12 + -1n) = 0

Subproblem 1

Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12

Subproblem 2

Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12

Solution

n = {12, 12}

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